Session 12_2, Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1: Import related libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 2: Load your dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1714</td>\n",
       "      <td>2.40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1664</td>\n",
       "      <td>2.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1760</td>\n",
       "      <td>2.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1685</td>\n",
       "      <td>2.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1693</td>\n",
       "      <td>2.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    SAT   GPA\n",
       "0  1714  2.40\n",
       "1  1664  2.52\n",
       "2  1760  2.54\n",
       "3  1685  2.74\n",
       "4  1693  2.83"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('Simple Linear Regression.csv')\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SAT</th>\n",
       "      <th>GPA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>84.000000</td>\n",
       "      <td>84.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1845.273810</td>\n",
       "      <td>3.330238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>104.530661</td>\n",
       "      <td>0.271617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1634.000000</td>\n",
       "      <td>2.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1772.000000</td>\n",
       "      <td>3.190000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1846.000000</td>\n",
       "      <td>3.380000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1934.000000</td>\n",
       "      <td>3.502500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2050.000000</td>\n",
       "      <td>3.810000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               SAT        GPA\n",
       "count    84.000000  84.000000\n",
       "mean   1845.273810   3.330238\n",
       "std     104.530661   0.271617\n",
       "min    1634.000000   2.400000\n",
       "25%    1772.000000   3.190000\n",
       "50%    1846.000000   3.380000\n",
       "75%    1934.000000   3.502500\n",
       "max    2050.000000   3.810000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3: Pick appropriate variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1714\n",
       "1    1664\n",
       "2    1760\n",
       "3    1685\n",
       "4    1693\n",
       "Name: SAT, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = data['GPA']\n",
    "x1 = data['SAT']\n",
    "x1.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 4: Plot your dataset and see what's happening"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1, y)\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 5: Select and create your model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>GPA</td>       <th>  R-squared (uncentered):</th>      <td>   0.996</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.996</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>2.120e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 18 Dec 2020</td> <th>  Prob (F-statistic):</th>          <td>9.38e-102</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>13:31:29</td>     <th>  Log-Likelihood:    </th>          <td>  12.440</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    84</td>      <th>  AIC:               </th>          <td>  -22.88</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    83</td>      <th>  BIC:               </th>          <td>  -20.45</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "   <td></td>      <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>SAT</th> <td>    0.0018</td> <td> 1.24e-05</td> <td>  145.594</td> <td> 0.000</td> <td>    0.002</td> <td>    0.002</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 9.848</td> <th>  Durbin-Watson:     </th> <td>   1.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.007</td> <th>  Jarque-Bera (JB):  </th> <td>  11.422</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.594</td> <th>  Prob(JB):          </th> <td> 0.00331</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.361</td> <th>  Cond. No.          </th> <td>    1.00</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                    GPA   R-squared (uncentered):                   0.996\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.996\n",
       "Method:                 Least Squares   F-statistic:                          2.120e+04\n",
       "Date:                Fri, 18 Dec 2020   Prob (F-statistic):                   9.38e-102\n",
       "Time:                        13:31:29   Log-Likelihood:                          12.440\n",
       "No. Observations:                  84   AIC:                                     -22.88\n",
       "Df Residuals:                      83   BIC:                                     -20.45\n",
       "Df Model:                           1                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "SAT            0.0018   1.24e-05    145.594      0.000       0.002       0.002\n",
       "==============================================================================\n",
       "Omnibus:                        9.848   Durbin-Watson:                   1.116\n",
       "Prob(Omnibus):                  0.007   Jarque-Bera (JB):               11.422\n",
       "Skew:                          -0.594   Prob(JB):                      0.00331\n",
       "Kurtosis:                       4.361   Cond. No.                         1.00\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#x = sm.add_constant(x1)\n",
    "model = sm.OLS(y,x1).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>const</th>\n",
       "      <th>SAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1693</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   const   SAT\n",
       "0    1.0  1714\n",
       "1    1.0  1664\n",
       "2    1.0  1760\n",
       "3    1.0  1685\n",
       "4    1.0  1693"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 6: Plot your regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RDz74IIYOHWrW8dvLAmhp0igveHt1QmL6OZTdqka3rh6YMSEQox7tbda55XL49A9IzDgPbV0DgHt/AIkZ5+Ht1cnmPoulqLt6oPRWtcHlarWX0f0r2rjY7Fg1AVhlYmF27sThwSG//O6OfQd3Vydo61o/SyG2fFJTq73M+vtoq54qKrUd/hzGjn349A9Gy2rsd2DK35Ic34scZA8aABAbG4s5c+YgJiYGSUlJmDp1KgDgwoULOHDgAHbs2IHi4mKzjm1qym1QH1+snaf/7mNbS6Xbsa9A9yNvoq1rwI59BQjq4ytTqaQjxZ3f5JH9Dd41Tx7ZX9T37desq8acd1FUfJGDhqCHAPzczZJ0VleW0lvVcFYBLs4qvZcjNZUv7fBFq975Nk8nNfXvw6+NLi0/b/cO/121d+y0wxf1vt/SW9V4P+ksKu/U6NWVsd+B2L8lptxaSVFREWpraxEYGAgPDw+Ehobi/Plf+n0zMjJQWlqK6Oho1NXVoaSkBM899xz+/ve/y1hq5bPnAX2p+sibtk099p1ZXXg7Vk0wseRA2YXvIfh2bbXcUDdLgwB0cXWCTxcXveAAwKYGbi3Z5dvescV2XRkb97HnvyVzyRo0rl69ioSEBOzatQsAkJWVhejoaN362NhYxMbG6radMWMGA4YI9jygL2Uf+YigHpg06gHRd4jmjFFMemUP/Hw82n2Yrq0L0N2aBrz/skZv2ZIPj9vUwK0ln95u79imjAm1N+5jz39L5pI1aGg0GuTn52Py5MlwdnZGaGgowsPDMWfOHMTGxiI4OFjO4tksexrQb8nad35STAhorGymXJhs8c7XkvNAtXVsqS729vy3ZC7ZxzQWLVqERYsW6S3bunVrq+169epl0Wc07ElHu16UzBp3fuYEitKSynan7WiPKRcm3vmKI9XFnvNctSZ70CDLMLXrxVZY6s7P3EAhRdlMuTDxzvceY8kQUl7sOWOuPk5YaMfsKaOjOUny5s2cOdbY9B3WyOm39nMDSvsdtUyGAO4FzpkTBst2cVdaHXWEsewpBg07Zk8/ZEnU1kLdq5vJu4mZ58meKe13JNXsvVJSWh11hKJTboksTVVWhm4PDjC+YQtNg9luLk6YWVDM7gkFscVkAHvCoEF2x/m/X8Pvd6bfcc5ald7qwmOtdFZOVSEekwHk5SR3AYik4JaZDnV3b6i7e4sOGI3d1IAgoLSkEqUllbLdwTb10Tedp+mBvdwC82ZBsHdRmoFwc9G/dDliMoBcGDTIZnXa9pEuUPg8P1XUPjVPR/0SJL4p0lvX1p2qpe9g23tgkVobEdQDMycM1n0v/t7usg6COxp2T5HNyC0oRuOqP2PykU9N2q/q9TdRvfB/jG4nVzprey2c2WuyO9RdZa/dXkyDlQ+DBilW0wXvxU/fxMiLOZhkwr4rpvwZ1x4aprvg7/k546a9C6fY3P6WF+IhA/2RX1Ru9oW5rT76JubOL2ULLxiy16Amhq1+dqbc2jFbTgN0Hj0KfgVfmbRP1s6D+DC/Wq+l4KwCVE6tZ4tt6s4wtY4MPSPQkqnPDIg5JmB6SqlUqamW+h0p8XkLc0nxO1LKZzeWcssxDVKMbj39fxnMFhkwnlm4SzdG8cm39QZni20eMICOjRcYGn9oydTjt+yjb4upA/JKT0115LEcW/7s7J4iWZk7c6ygune/0/xCa8rF0NwLp9j9OvKGPXPnsDK0vZJTU5Ue1CzJlj87gwZZnRQzxwKtB6mNjQ00Z+6FU+w5OnJhlmpAXunzVCk9qFmSLX92dk+RVTR1O5kSMKKXpmHin1J1AcNZBXh63LvPMZRmaSh/v+kNeM115MJp6BwtdfTCLFVKqdJTUx35eQtb/uxsaZDFdHTm2JkmZpe0lf1kaJm5F05D5+ho9lRb55HqRUVKCRItyTXtuBKylmx5ynVmT9kxObKnpJhi3JpsOcPMWuypjiyVtWRPdcQJC8myGhuh7uFr8m6OPnMsyUPK1wU7KgYNMt1PP0Hdz/Q/MAYKkpstZy0pheRB49///jeSk5ORkJAg9aEdnpx9sarycnQL7G/SPg3390TF2XMWKhGR6Ww5a0kpJAkaN27cwO7du7Fnzx7cuHHDpH03bdqEzMxMqFQqTJkyBS+88ILe+kOHDuH999+HIAjo1asX4uPj4eNj+hvX5NbRC74cU0I4X/oWfsN/Y9I+2rCJqNxh2txQRNai9DRkW2B20Kivr0dWVhaSk5ORm5uLxsZGCIKAfv36ISoqStQx8vLycOLECaSlpaG+vh5hYWHQaDQYMODeS3OqqqqwatUq7N69GwEBAdi0aRPef/99xMXFmVtsWUhxwbdWX6zLiVx0nTTOpH3u/u8y/LT0VcnKQGQptpy1pBQmB41Lly4hOTkZn3/+OW7dugUA8PDwQFhYGKKiovCb34i/Mx02bBgSExPh4uKCmzdvoqGhAZ07d9atr6urw8qVKxEQEAAAGDRoEPbu3WtqkWUnxQXfkn2x7qm74T33BeMbNnP7b7tQOyG8w+cGpO12U0I6JSmbktOQbYGooFFTU4P09HQkJyfjzJkzEAQBzs7OePzxx3H8+HFMmjQJq1atMqsArq6uSEhIwPbt2zF+/HhdgACArl27YuzYsboybNmyBc8//7xJx28vdcxaKtq4sFdUaqFWe4k6hrqrB0pvVRtc3t4x2ly3Zg2wfLmoc+t8/TXw0EMAAKk6CA+f/gGJGeehrWsAcC8IJmach7dXJ4x6tLdVjiX2O3BkrCPjHKWO2g0a//3vf5GcnIx//etfqKqqAgAMHToUERERCAsLg7+/PwYPHtzhQsTGxmLOnDmIiYlBUlISpk7Vf6HOnTt3sGDBAgwePBiRkZEmHVsJz2n4tTH45uftrsvtNnaHPHlkf4N9sZNH9m8zP7xl7niXV5eg818/MqnsM+Zuxy1Pv3szowb0BSTIRW/+WZ1UQMuvR1vXgB37ChDUx7RU3h37CnQBQ+yxrJ1fb6mWkCVbWPb0DIKl2FMddeg5jSlTpsDJyQkPPfQQxo4diwkTJqBXr16SFa6oqAi1tbUIDAyEh4cHQkNDcf78eb1tSkpK8Mc//hHDhw/Hq6/aZr+5scE3MWMe5vbF+vz+abgd+cKk8v5+4S7UuHnoLZMqJbHlZ20rnptzPqWnU1oqmcEW3ptB9sNo95Sbmxu6du0KNzc3aLXS/vFdvXoVCQkJ2LVrFwAgKysL0dHRuvUNDQ2IiYnBhAkT8NJLL0l6bmsydsEXO+Yhti/WZ9J4uJ3IAQC4iSxj6fUKwMUFSz48jhoLpiSKmVrc3PMpPZ3SUskMfGCNrKndoJGUlITU1FTs378fR44cgUqlwq9+9StMnDgR4eHh6NmzZ4dOrtFokJ+fj8mTJ8PZ2RmhoaEIDw/HnDlzEBsbi+LiYnzzzTdoaGhAZmYmAOChhx7CW2+91aHzyqG9C74Ud8j+g/vBqaLCpDKV3rwNqPQn87N0SqKYz2Tu+ZSeTmmplpDSW1hkX9oNGkOGDMGQIUOwfPlyHD58GKmpqTh69Cg2btyId999F0OHDoVKpUJHpq9atGgRFi1apLds69atAIDg4GAUFhaafWxbYe4dsiXmebJ0SmJbn7VpbKMj51N6OqWlWkJKb2GRfTF5wsLbt29j3759+Pzzz5Gfnw8AcHZ2xvDhwzFx4kSMHTsWXbp0sUhhzaGEgXBjTJlEzdYmBGxJaa+5tOYApqU+u6Xr1J4GeS3FnurI2EB4h2a5vXz5MlJSUrB3715cv34dKpUK7u7uGDNmDDZs2GDuYSVlC0EDaD/7xdxAodQfspKepWD2lHFK/R0piT3VkWRBo7a2FpWVlfD19YWLS+terby8PKSkpODAgQP46aefcO6cMuYcspWgoUcQoA4w7UkIQ/M82dMP2VIXRXuqI0thHRlnT3XU4anRCwsLsW7dOpw8eRKNjY1wc3PD6NGjsXTpUtx///267YYNG4Zhw4Zh1apVOHTokDSldyT19VDf72faLgN/hVu5X1moQMrBlFIi5Wj3vZVFRUWYPn06cnJyoFKp4Ofnh9raWmRkZOCZZ57BzZs3W+3j7u6O8HBpppewezU1v7wGVWTA0EY8jdKSSpSWVDpEwADaTyklIutqN2h89NFHuHv3Ll555RWcOnUKx48fx5dffonnn38eZWVl2L59u7XKaTdUlbd/CRR9uovap+qNt3WBonL7JxYuofIwpZRIOdrtnjp16hQ0Gg3mzZunW+bp6YkVK1bg7NmzOH78uMULaBdqauC15GV0+uffRe9y+69/Q+0k06ZMsVdMKSVSjnZbGmVlZRg0aJDBdY8++iiuX79ukULZhaoqeC7/X12LQkzAqMg6pmtRMGD8IkozEG4u+j9VJT20R+RI2m1p1NbWws3N8EQUnp6eqK5uPeuqI1P9eAuer7+KTv8Q/xKi8q8voDHAuoO5UmQiWTNtVukP7RE5Er4jvINUJSXwfHUJOqWliN6n7NsfIHjL8/ZBKTKR5Mhmahk4mgbBGTiIrKvd7ikyzOnaVXg/NwXq7t7o9tCvjAaMqtVrUHrjlq7rSa6AAUiTiSRHNlNToGoa22gKVLkFxRY7JxG1ZrSloWoxoZ2jcrpUBK9XFsItV9zg/513N6PmuedbTQgoNykykeTIZuJMrkTKYDRobN68GZs3b25zfWBgYKtlKpUK33zzTcdKpgDO3xTAK3Y+XPPPGt1WUKlw56Pt0D4dpbhA0ZwUmUhyZDMx7ZZIGdoNGs2f+HYkbvv3wWfWc0a3a+ziiTt/2YbacROsUCppSDF9uBxTkDPtlkgZ2g0a2dnZ1iqHYqhu/wjvP7b9HvKG7gG4839/Rd2TGiuWSjpSZCLJkc2k9HdlEDkKk7KntFot3N3v3dkVFha2eteFSqVCREQEnJ2dpSuhtTk5odG/G5xLfpkipb7/ANz5YAvqHxsmY8GkI/YNgJY+hqnnA5h2SyQ3UUHj008/xV//+ldER0dj4cKFAIBDhw7hgw8+0G0jCAJUKhWKi4v1niC3NYKXN35Mz4LrsaOoDx6KhoeC5S6SIskxvbm1AxURtWY0aKxYsQJ79uxBly5dDD7ot2zZMgBAY2Mj/vKXv+Avf/kLpk2bBh8f+dJKO6qxdx9on/2D3MVQLM46S+S42g0ax48fx+7du/HEE09gw4YN8PX1bbXNzJkzdf/t5eWFuLg47N69G7Nnz5a+tKQItpT+qqQXPrXHVspJ1O7DfZ999hm8vLywceNGgwGjpcjISPj7++Po0aOiC7Bp0yaEhYUhPDwcH3/8cav1586dQ1RUFMaNG4cVK1agvr5e9LHJMiyV/vpJZiFeXJuN2Wuy8eLabHyS2bH3w9vKA4G2Uk4iwEjQOHPmDEJCQkR3NTk7O2PkyJH49ttvRW2fl5eHEydOIC0tDbt378Ynn3yCS5cu6W2zZMkSvP7668jMzIQgCEhKShJ1bLKcttJcO5L++klmIb44cx1NL1lsFIAvzlzvUOCwlfdw2Eo5iQAjQaO8vBy9evUyuG7QoEGIiIhotTwgIAC3b98WdfJhw4YhMTERLi4uKC8vR0NDAzp37qxbf+3aNdTU1ODhhx8GAERFRSEjI0PUsclyLDHr7JGzhmdMbmu5GLbyQKCtlJMIMDKm4e3tjbt37xpcN3bsWIwdO7bV8h9//BF+fuJfW+rq6oqEhARs374d48ePR0BAgG5dSUkJ1Gq17t9qtdrg2wLb0967bh2BWu0l+TEnjfKCt1cnJKafQ9mtanTr6oEZEwIx6tHeZh+zrde4NwrmfwZ1Vw+U3mo9E7O6q4feMS1RR6YQW045KaUcSuYodWT0ifCvvjLtlaInT55Enz59TNonNjYWc+bMQUxMDJKSkjB16lQA9zKyms991ZTWa4ry8io0tnVFsnOWfNl9UB9frJ03Qm9ZR87lpDIcOJxU5h938sj+Bh8InDyyv+6YlqwjscSUU05KqCOls6c6cnJStXuz3W731JgxY3Du3DmcOHFC1MkOHjyI77//HuPGjRO1fVFREc6dOwcA8PDwQGhoKM6fP69b36NHD5SWlur+XVZWhu7dxb0ilWyL5mHDU9a0tVyMEUE9MHPCYN1Yi7+3O2ZOGKy4rCRbKScRYKSlETzT4KcAABJUSURBVBUVha1bt+JPf/oTNmzYgBEjRrS57alTpxAXFwd/f39MmjRJ1MmvXr2KhIQE7Nq1CwCQlZWF6Oho3fqePXvC3d0dp0+fxqOPPorPP/8cISEhoo5NtuX5cYMB3BvDaBTutTA0D9+vW24uW3kg0FbKSaQSBKHdvpuMjAy88sorAIBRo0Zh7NixeOCBB+Dj44Pbt2/jypUrOHDgAA4dOgRBELB161Y88cQTogvw/vvvIz09Hc7OzggNDcWiRYswZ84cxMbGIjg4GIWFhYiLi0NVVRWCgoIQHx/f5tsEDWH3lH00mS2FdWQc68g4e6ojY91TRoMGAOTk5CAuLg7Xr183OKYgCAICAgKwbt06/Pa3v+1YiSXGoGEfP2RLYR0Zxzoyzp7qyFjQEDX31OOPP47MzEwcOXIEWVlZuHLlCsrLy+Hr64uePXtizJgxGDNmjG4yQyIisk+iZ7l1dXXFU089haeeesqS5SEiIgXjO8KJiEg0Bg0iIhLNpJcwkbQ4sykR2RoGDZnwnRREZIvYPSUTzmxKRLaIQUMmnNmUiGwRg4ZMLPFOCiIiS2PQkIkl3klBRGRpHAiXSdNgN7OniMiWMGjIiDObEpGtYfcUERGJxqBBRESiMWgQEZFoHNOwYZyGhIisjUHDRnEaEiKSA7unbBSnISEiOTBo2ChOQ0JEcpA9aGzevBnh4eEIDw/HunXrWq0vKChAdHQ0Jk2ahHnz5qGyslKGUioPpyEhIjnIGjRycnJw7NgxpKSkIDU1FQUFBTh48KDeNm+99RZiY2ORlpaG/v37Y9u2bTKVVlk4DQkRyUHWgXC1Wo1ly5bBzc0NADBw4EBcv35db5vGxkbcvXsXAFBdXQ0fHx+rl1OJOA0JEclBJQiCIHchAODy5ct49tlnsWvXLvTr10+3/OzZs5g9ezY6d+4MDw8PJCUloWvXrvIVlIjIgSkiaFy8eBHz5s3DokWLEBkZqVteU1OD6OhoxMfHY8iQIfj444+Rm5uLLVu2iD52eXkVGhtl/4iyUKu9UFp6R+5iKBrryDjWkXH2VEdOTir4+3u2vd6KZTHo9OnTmDVrFhYvXqwXMADgwoULcHd3x5AhQwAAU6dORV5enhzFJCIiyBw0bty4gQULFmD9+vUIDw9vtb5v374oLi7GpUuXAABZWVkIDg62djGJiOhnsg6Eb9u2DVqtFmvWrNEtmzZtGrKzsxEbG4vg4GDEx8fj5ZdfhiAI8Pf3x9tvvy1jiYmIHJsixjQsiWMa9tHPaimsI+NYR8bZUx0ZG9Pg3FM2gpMTEpESMGjYAE5OSERKIXv2FBnHyQmJSCkYNGwAJyckIqVg0LABnJyQiJSCQcMGcHJCIlIKDoTbAE5OSERKwaBhI0YE9WCQICLZsXuKiIhEY9AgIiLRGDSIiEg0Bg0iIhKNQYOIiERj0CAiItEYNIiISDQGDSIiEo1Bg4iIRGPQICIi0Rg0iIhINNnnntq8eTPS09MBABqNBkuXLtVbf+nSJaxcuRK3b9+GWq3Gxo0b4ePjI0dRiYgcnqwtjZycHBw7dgwpKSlITU1FQUEBDh48qFsvCALmz5+POXPmIC0tDYGBgdiyZYuMJSYicmyytjTUajWWLVsGNzc3AMDAgQNx/fp13fqCggJ07twZISEhAICYmBhUVlbKUlYiIgJUgiAIchcCAC5fvoxnn30Wu3btQr9+/QAA+/fvR0pKCtRqNc6dO4cBAwbgtddeg6+vr7yFJSJyULKPaQDAxYsXMW/ePCxdulQXMACgvr4eeXl52LlzJ4KDg/Hee+9hzZo1WLNmjehjl5dXobFREXHR6tRqL5SW3pG7GIrGOjKOdWScPdWRk5MK/v6eba+3YlkMOn36NGbNmoXFixcjMjJSb51arUbfvn0RHBwMAIiIiEB+fr4cxSQiIsgcNG7cuIEFCxZg/fr1CA8Pb7X+kUceQUVFBQoLCwEA2dnZCAoKsnYxiYjoZ7J2T23btg1arVavu2natGnIzs5GbGwsgoOD8cEHHyAuLg7V1dXo0aMH1q1bJ2OJiYgcm2IGwi2FYxr20c9qKawj41hHxtlTHRkb01DEQDg5rtyCYuw5UoTySi38vd0RpRmIEUE95C4WEbWBQYNkk1tQjL+lF6K2vhEAUF6pxd/S741fMXAQKZPs2VPkuPYcKdIFjCa19Y3Yc6RIphIRkTFsaVgJu2FaK6/UmrSciOTHloYVNHXDNF0Mm7phcguKZS6ZvPy93U1aTkTyY9CwAnbDGBalGQg3F/2foJuLE6I0A2UqEREZw+4pK2A3jGFN3XPstiOyHQwaVuDv7W4wQLAb5l7gYJAgsh3snrICdsMQkb1gS8MK2A1DRPaCQcNK2A1DRPaA3VNERCQagwYREYnGoEFERKIxaBARkWgMGkREJBqDBhERicagQUREojFoEBGRaLI/3Ld582akp6cDADQaDZYuXWpwu8OHD+ONN95Adna2NYtn1/iODyIylawtjZycHBw7dgwpKSlITU1FQUEBDh482Gq7srIyrF27VoYS2i++44OIzCFr0FCr1Vi2bBnc3Nzg6uqKgQMH4vr16622i4uLw8KFC2Uoof3iOz6IyByydk898MADuv++fPky0tPTsWvXLr1tEhMT8eCDD2Lo0KFmncPf37NDZbR1arWXweUVbbzLo6JS2+Y+9srRPq85WEfGOUodyT6mAQAXL17EvHnzsHTpUvTr10+3/MKFCzhw4AB27NiB4mLzuk3Ky6vQ2ChIVFLbolZ7obT0jsF1fm2848PP273NfexRe3VE97COjLOnOnJyUrV7sy179tTp06cxa9YsLF68GJGRkXrrMjIyUFpaiujoaMydOxclJSV47rnnZCqpfeE7PojIHCpBEGS7Db9x4wYiIyPx7rvvYsSIEe1ue/XqVcyYMcPk7Cm2NNq++2H2lH3dIVoK68g4e6ojYy0NWbuntm3bBq1WizVr1uiWTZs2DdnZ2YiNjUVwcLCMpbN/fMcHEZlK1paGNbClYR93P5bCOjKOdWScPdWR4sc0iIjIdjBoEBGRaAwaREQkmiKe07AkJyeV3EWQlaN/fjFYR8axjoyzlzoy9jnsfiCciIikw+4pIiISjUGDiIhEY9AgIiLRGDSIiEg0Bg0iIhKNQYOIiERj0CAiItEYNIiISDQGDSIiEo1BwwZVVVUhIiICV69exZEjR/D000/r/jd8+HDMmzcPAHDu3DlERUVh3LhxWLFiBerr6wEA169fx/Tp0zF+/HjMnz8fd+/elfPjWETzOgKAY8eOYdKkSYiIiMDSpUtRW1sLgHXUvI727NmDsLAwTJw4EatXr9bVhaPW0ebNmxEeHo7w8HCsW7cOAJCTk4OJEyciNDQU7777rm5bh6ojgWzK2bNnhYiICCEoKEj44Ycf9NaVlJQIY8aMEb777jtBEAQhPDxcOHPmjCAIgrB8+XLh008/FQRBEObOnSvs27dPEARB2Lx5s7Bu3TrrfQArMFRHISEhwrfffisIgiAsWrRISEpKEgSBddRUR0VFRcKTTz4p3Lx5UxAEQVi5cqWwfft2QRAcs46OHz8uTJ06VdBqtUJtba0wY8YMYe/evYJGoxGuXLki1NXVCbNnzxYOHz4sCIJj1RFbGjYmKSkJK1euRPfu3VutW7duHaZNm4Z+/frh2rVrqKmpwcMPPwwAiIqKQkZGBurq6vDll19i3LhxesvtiaE6amhoQFVVFRoaGqDVauHu7s46alZH58+fx8MPP6z79+jRo3Ho0CGHrSO1Wo1ly5bBzc0Nrq6uGDhwIC5fvoy+ffuid+/ecHFxwcSJE5GRkeFwdWT3s9zam7feesvg8suXLyMvL0+3vqSkBGq1WrderVbj5s2buHXrFjw9PeHi4qK33J4YqqNVq1bh+eefh6enJ3r16oXx48ejoKCAdfSzwYMHY82aNbhx4wa6d++OjIwMlJWVOezv6IEHHtD99+XLl5Geno4//OEPenXRvXt33Lx50+HqiC0NO/HPf/4Tzz33HNzc3AAAjY2NUKl+meJYEASoVCrd/zfX8t/2prS0FOvXr8e+fftw7NgxDB06FPHx8ayjZvr374/Fixdj/vz5mD59OgYNGgRXV1eHr6OLFy9i9uzZWLp0KXr37m2wLhytjhg07ERWVhbCwsJ0/+7RowdKS0t1/y4rK0P37t3h5+eHO3fuoKGhAcC9C6qhri57curUKfz6179Gnz594OTkhGeeeQZ5eXmso2a0Wi2GDBmC1NRU/OMf/0BAQAB69+7t0HV0+vRpzJo1C4sXL0ZkZGSrumj6zI5WRwwadqCiogI1NTXo3bu3blnPnj3h7u6O06dPAwA+//xzhISEwNXVFY899hj2798PAEhNTUVISIgs5baWX//618jPz0dZWRmAewE2ODiYddTMTz/9hFmzZqGqqgq1tbXYuXMnwsLCHLaObty4gQULFmD9+vUIDw8HAAwdOhTfffcdvv/+ezQ0NGDfvn0ICQlxuDriS5hs1O9+9zskJiaiV69eyM/Px+rVq5GUlKS3TWFhIeLi4lBVVYWgoCDEx8fDzc0N165dw7Jly1BeXo777rsPGzduhI+Pj0yfxHKa11FKSgq2bt0KZ2dn9O3bF2+88Qb8/PxYR83qKDk5GTt27EB9fT0iIiKwaNEiAI75O1q9ejV2796NPn366JY1JZnEx8dDq9VCo9Fg+fLlUKlUDlVHDBpERCQau6eIiEg0Bg0iIhKNQYOIiERj0CAiItEYNIiISDROI0LUAVlZWUhKSkJ+fj7u3LkDX19fBAcHY8qUKRgzZkyb+23ZsgUbNmyAr68v/v3vf+ue5AfuzTa7fPly0WU4f/58hz4DkSkYNIjM9Oabb2Lnzp3o2bMnxowZg65du+LmzZs4cuQIsrOz8cwzz+DNN980uG9aWho8PDzw448/4sCBA4iIiNCtCwwMxMKFC/W2P3ToEAoLCxEZGYmePXta9HMRtYdBg8gMJ0+exM6dOzFu3Dhs3LhRNykdANy5cwczZsxAUlISNBoNnnrqKb19//vf/+LixYuIiYnBtm3bkJyc3CpoBAYG6u1z7do1XdD47W9/a9kPR9QOjmkQmeHw4cMAgOnTp+sFDADw8vLC4sWLAQAHDx5stW9qaioAYNy4cRg+fDhOnjyJH374wbIFJpIIgwaRGerq6gAAFy5cMLj+sccew3vvvYdZs2bpLa+vr8f+/fvRrVs3BAYGIiwsDIIg4LPPPrN0kYkkwaBBZIYnnngCALB27Vq8+eabOHPmjG42UwDo1KkTJkyY0Kqb6ejRoygvL8f48eOhUqkwduxYuLm5Yc+ePXr7EykVgwaRGUaPHo1nn30WdXV12LlzJ6ZNm4Zhw4Zh7ty52LFjB4qLiw3u19Q11TRzqpeXFzQaDUpKSnDkyBGrlZ/IXAwaRGZatWoVPvroIzz55JNwdXVFVVUVjhw5gvj4eDz11FPYsGEDGhsbddtXVlbiiy++QM+ePfHII4/oljcNgicnJ1v9MxCZitlTRB0watQojBo1Cnfv3sWpU6eQm5uL7OxsfP/999iyZQsaGxuxZMkSAEB6ejpqa2sRFham9wa30aNHw9PTE0ePHkVJSYldvKiH7BdbGkQS6NKlCzQaDZYtW4bMzEysXr0aKpUKO3fuRHV1NYBfuqa2bt2KQYMG6f43ZMgQVFVVob6+HikpKXJ+DCKj2NIgMlFVVRWioqLQv39/fPTRR63Wq1Qq/P73v0dGRgaOHTuG4uJiuLi44KuvvkJAQABGjRrVap+7d+9i3759+OyzzzB37ly7eJc02ScGDSITeXp64s6dO8jJyUFZWRm6devW5rZOTk5Qq9X4+OOPAdx7+9tLL71kcNuvv/4a33//PU6ePInhw4dbpOxEHcXuKSIzTJ8+HbW1tYiNjUVJSUmr9VlZWcjJycHYsWPh6emJtLQ0AMDEiRPbPGZkZCQADoiTsrGlQWSG+fPn48KFC8jMzERoaChGjhyJfv36ob6+Hv/5z3/w1VdfYcCAAVi1ahVOnTqFK1eu4JFHHkHv3r3bPGZkZCQSEhJw8OBB3L592+bfJU32iS0NIjM4OzsjISEBmzdvxpNPPomvv/4aiYmJSE5OhlarxeLFi5GSkgI/Pz9dK2PSpEntHrNHjx54/PHHodVqdfsQKY1KEARB7kIQEZFtYEuDiIhEY9AgIiLRGDSIiEg0Bg0iIhKNQYOIiERj0CAiItEYNIiISDQGDSIiEo1Bg4iIRGPQICIi0f4/4OF4+3wRLwAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat = 0.0017*x1 + 0.275\n",
    "fig = plt.plot(x1,yhat,  lw=3, c='red')\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y)\n",
    "yhat = 0.0017*x1 + 0\n",
    "fig = plt.plot(x1,yhat,  lw=3, c='red')\n",
    "plt.xlabel('SAT', fontsize = 20)\n",
    "plt.ylabel('GPA', fontsize = 20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}